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Engineering analysis requires the prediction of (say, a single) selected “output” se relevant to ultimate component and system performance:∗ typical outputs include energies and forces, critical stresses or strains, flowrates or pressure drops, and various local and global measures of concentration, temperature, and flux. These outputs are functions of(More)
We present a technique for the rapid and reliable prediction of linear-functional outputs of coercive and non-coercive linear elliptic partial differential equations with affine parameter dependence. The essential components are: (i) rapidly convergent global reduced basis approximations – (Galerkin) projection onto a space WN spanned by solutions of the(More)
We present reduced basis approximations and associated rigorous a posteriori error bounds for parametrized saddle point problems. First, we develop new a posteriori error estimates that, unlike earlier approaches, provide upper bounds for the errors in the approximations of the primal variable and the Lagrange multiplier separately. The proposed method is(More)
The optimization, control, and characterization of engineering components or systems require fast, repeated, and accurate evaluation of a partial-differential-equation-induced input – output relationship. We present a technique for the rapid and reliable prediction of linear–functional outputs of elliptic partial differential equations with affine parameter(More)
We present reduced basis approximations and associated rigorous a posteriori error bounds for the instationary Stokes equations. The proposed method is an extension of the penalty approach introduced in Gerner and Veroy (2011b) to the time-dependent setting: The introduction of a penalty term enables us to develop a posteriori error bounds that do not rely(More)
We present an efficient model order reduction method [1] for parametrized elliptic variational inequalities of the first kind: find u ∈ K such that: a(u, v − u;μ) ≥ f(v − u;μ), ∀v ∈ K(μ) where K(μ) := {v ∈ H1(Ω)|Bv ≤ g(μ)}. Motivated by numerous engineering applications that involve contact between elastic body and rigid obstacle, e.g. the obstacle problem(More)
In this paper, we consider the efficient and reliable solution of distributed optimal control problems governed by parametrized elliptic partial differential equations. The reduced basis method is used as a low-dimensional surrogate model to solve the optimal control problem. To this end, we introduce reduced basis spaces not only for the state and adjoint(More)
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